SPARSKIT: A basic tool kit for sparse matrix computations

Presented here are the main features of a tool package for manipulating and working with sparse matrices. One of the goals of the package is to provide basic tools to facilitate the exchange of software and data between researchers in sparse matrix computations. The starting point is the Harwell/Boeing collection of matrices for which the authors provide a number of tools. Among other things, the package provides programs for converting data structures, printing simple statistics on a matrix, plotting a matrix profile, and performing linear algebra operations with sparse matrices

Numerical solution of large Lyapunov equations

A few methods are proposed for solving large Lyapunov equations that arise in control problems. The common case where the right hand side is a small rank matrix is considered. For the single input case, i.e., when the equation considered is of the form AX + XA(sup T) + bb(sup T) = 0, where b is a column vector, the existence of approximate solutions of the form X = VGV(sup T) where V is N x m and G is m x m, with m small is established. The first class of methods proposed is based on the use of numerical quadrature formulas, such as Gauss-Laguerre formulas, applied to the controllability Grammian. The second is based on a projection process of Galerkin type. Numerical experiments are presented to test the effectiveness of these methods for large problems

On the parallel solution of parabolic equations

Parallel algorithms for the solution of linear parabolic problems are proposed. The first of these methods is based on using polynomial approximation to the exponential. It does not require solving any linear systems and is highly parallelizable. The two other methods proposed are based on Pade and Chebyshev approximations to the matrix exponential. The parallelization of these methods is achieved by using partial fraction decomposition techniques to solve the resulting systems and thus offers the potential for increased time parallelism in time dependent problems. Experimental results from the Alliant FX/8 and the Cray Y-MP/832 vector multiprocessors are also presented

Asymptotic behaviour of the inductance coefficient for thin conductors

We study the asymptotic behaviour of the inductance coefficient for a thin toroidal inductor whose thickness depends on a small parameter \eps>0. We give an explicit form of the singular part of the corresponding potential u\ue which allows to construct the limit potential $u$ (as \eps\to 0) and an approximation of the inductance coefficient L\ue. We establish some estimates of the deviation u\ue-u and of the error of approximation of the inductance. We show that L\ue behaves asymptotically as \ln\eps, when \eps\to 0

#Halal Culture on Instagram

Halal is a notion that applies to both objects and actions, and means permissible according to Islamic law. It may be most often associated with food and the rules of selecting, slaughtering, and cooking animals. In the globalized world, halal can be found in street corners of New York and beauty shops of Manila. In this study, we explore the cultural diversity of the concept, as revealed through social media, and specifically the way it is expressed by different populations around the world, and how it relates to their perception of (i) religious and (ii) governmental authority, and (iii) personal health. Here, we analyze two Instagram datasets, using Halal in Arabic (325,665 posts) and in English (1,004,445 posts), which provide a global view of major Muslim populations around the world. We find a great variety in the use of halal within Arabic, English, and Indonesian-speaking populations, with animal trade emphasized in first (making up 61% of the language's stream), food in second (80%), and cosmetics and supplements in third (70%). The commercialization of the term halal is a powerful signal of its detraction from its traditional roots. We find a complex social engagement around posts mentioning religious terms, such that when a food-related post is accompanied by a religious term, it on average gets more likes in English and Indonesian, but not in Arabic, indicating a potential shift out of its traditional moral framing

Some fast elliptic solvers on parallel architectures and their complexities

The discretization of separable elliptic partial differential equations leads to linear systems with special block triangular matrices. Several methods are known to solve these systems, the most general of which is the Block Cyclic Reduction (BCR) algorithm which handles equations with nonconsistant coefficients. A method was recently proposed to parallelize and vectorize BCR. Here, the mapping of BCR on distributed memory architectures is discussed, and its complexity is compared with that of other approaches, including the Alternating-Direction method. A fast parallel solver is also described, based on an explicit formula for the solution, which has parallel computational complexity lower than that of parallel BCR

Solving large sparse eigenvalue problems on supercomputers

An important problem in scientific computing consists in finding a few eigenvalues and corresponding eigenvectors of a very large and sparse matrix. The most popular methods to solve these problems are based on projection techniques on appropriate subspaces. The main attraction of these methods is that they only require the use of the matrix in the form of matrix by vector multiplications. The implementations on supercomputers of two such methods for symmetric matrices, namely Lanczos' method and Davidson's method are compared. Since one of the most important operations in these two methods is the multiplication of vectors by the sparse matrix, methods of performing this operation efficiently are discussed. The advantages and the disadvantages of each method are compared and implementation aspects are discussed. Numerical experiments on a one processor CRAY 2 and CRAY X-MP are reported. Possible parallel implementations are also discussed